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arXiv · 2010.09165

Optimal Descartes' Rule of Signs for Circuits

Frédéric Bihan·Alicia Dickenstein·Jens Forsgård
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Abstract

We present an optimal version of Descartes' rule of signs to bound the number of positive real roots of a sparse system of polynomial equations in n variables with n+2 monomials. This sharp upper bound is given in terms of the sign variation of a sequence associated to the exponents and the coefficients of the system.

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Frédéric Bihan, Alicia Dickenstein, Jens Forsgård. 2020-10-19. Optimal Descartes' Rule of Signs for Circuits. https://arxiv.org/abs/2010.09165

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